If s1 is the variance of a small sample, and s2 is the variance of a larger sample from the same population. Is s1 an unbiased estimator for s2?
I am thinking since a sample variance is an unbiased estimator of the population variance, then s1 and s2 are both unbiased estimators for sigma^2, so s1 and s2 should also be unbiased estimators for each other.
But all the observations in a sample are part of the population, yet the observations between samples doesn't necessarily include each other. Does this make their variances biased?